Pareto optimality

Pareto optimality (or Pareto efficiency) describes a state of resource allocation in which no individual can be made better off without making another worse off. It is a concept from welfare economics that puts efficiency before fairness: an allocation is Pareto-optimal when all resources are fully used and nothing is wasted.

Formally, a point $x$ in an objective space is Pareto-optimal if there is no feasible alternative $y$ such that

$f_i(y) \geq f_i(x) \quad \forall i \in \text{objectives} \qquad \text{and} \qquad f_j(y) > f_j(x) \text{ for at least one objective } j$

(assuming maximization).

Applied to the blockchain trilemma, the three objectives are decentralization, security, and scalability. Since no configuration can maximize all three, the interesting answer is not a single winner but the set of configurations that nothing else dominates — the Pareto front.

How BlockchainBench computes this from raw simulation metrics, including normalization and a fully worked example, is described in How the Pareto calculation works.